The forest sector can play a pivotal role in mitigating climate warming by decreasing emissions to the atmosphere and increasing carbon removals. In an expanding bioeconomy, the pulp and paper industry provides opportunities for various low‐carbon wood products with promising substitution effects. However, assessing climate effects of wood product systems is complex and requires a holistic approach. The objective of this study was to advance time dynamic climate impact assessment of a bioeconomically promising wood product from a system perspective. For this purpose, a time dynamic life cycle assessment was conducted on a pulp‐based beverage carton. The assessment included fossil value chain emissions from cradle to grave, effects from biogenic carbon in a eucalyptus plantation, and credits from substitution. A polyethylene terephthalate (PET) bottle was considered for material substitution (MS) and differing marginal electricity and heat mixes for energy substitution. The results revealed dominating climate warming from value chain emissions and slight offsetting by biogenic carbon from standing biomass and soil organic carbon, and short‐term carbon storage in the beverage carton. MS and displacing marginal energy mixes transformed the climate warming into a substantial total cooling effect. However, substitution effects varied strongly in terms of substitution factors and temperature change with varying replacement rate of the beverage carton and different marginal energy mixes. A climate cooling range of −0.8 · 10−15 to −1.8 · 10−15 K per unit of beverage carton by 2050 was found, highlighting potential relevance for climate policy making. Thus, production and use of wood‐based beverage cartons over PET bottles can have climate cooling effects. Further assessments on alternative forestry systems (e.g., Nordic forests) are needed to identify the role of biogenic carbon in holistic climate assessments, with dynamic substitution effects included to increase the validity.